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Spin splitting in low-symmetry quantum wells beyond Rashba and Dresselhaus terms

Spin-orbit interaction in semiconductor structures with broken space inversion symmetry leads to spin splitting of electron and hole states even in the absence of magnetic field. We discover that, beyond the Rashba and Dresselhaus contributions, there is an additional type of the zero-field spin splitting which is caused by the interplay of the cubic shape of crystal unit cell and macroscopic structure asymmetry. In quantum wells grown along low-symmetry crystallographic axes, this type of spin-orbit interaction couples the out-of-plane component of carrier's spin with the in-plane momentum while the coupling strength is controlled by structure inversion asymmetry. We carry out numerical calculations and develop an analytical theory, which demonstrate that this interaction can dominate $\boldsymbol{k}$-linear spin splitting of heavy-hole subbands.